Dynamical systems arising from random substitutions

Rust, Dan and Spindeler, Timo (2018). Dynamical systems arising from random substitutions. Indagationes Mathematicae, 29(4) pp. 1131–1155.

DOI: https://doi.org/10.1016/j.indag.2018.05.013

Abstract

Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently replaced by a word from a finite set of possible words according to a probability distribution. We discuss the subshifts associated with such substitutions and explore the dynamical and ergodic properties of these systems in order to establish the groundwork for their systematic study. Among other results, we show under reasonable conditions that such systems are topologically transitive, have either empty or dense sets of periodic points, have dense sets of linearly repetitive elements, are rarely strictly ergodic, and have positive topological entropy.

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About

• Item ORO ID
• 70946
• Item Type
• Journal Item
• ISSN
• 0019-3577
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications	CRC 1283	Bielefeld University

• Keywords
• Primitive substitutions; random substitutions; symbolic dynamics
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2018 Royal Dutch Mathematical Society
• Depositing User
• Dan Rust